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Op amps problem Gain Calculation

Discussion in 'Beginner Electronics' started by N, Jul 4, 2005.

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  1. N

    N Guest

    Hi,
    Note to view the schematic below, change your font to fixed Courier.


    I have a problem I am trying to work out on simple Op Amps gain,
    and I am having trouble trying to prove what the gain is.
    I know what the gain is supposed to be (see below), but
    I am stumped as to how to actually go about proving it. When
    I try to setup the Kirchoff node equations I get a really
    ugly polynomial.

    I can put the design into a spice deck and prove it, but I want to
    understand the design from an analytical point of view.

    Gain = 2*R2/R1 * (1 + R2/Rg)(V2-V1) (GAIN FOR THE OP AMP BELOW)

    Now looking at the above equation it is obvious if you
    eliminate resistor Rg, the equation becomes a simple
    differential amplifier gain, which I can easily solve and
    prove. However when you add the positive feedback from
    the output, you get a different Beta for the loop gain
    that is hard to figure out.

    Anybody want to take a stab at proving this?

    Nick ------------
    | |
    V1---------R1-----------------------R2-------R2---| |
    | | |
    | ___ | |
    | | \ | |
    |--Vn| \ | |
    | \ Vout | Rg
    | |------------------ |
    |--Vp| / |
    | | _ / -----------
    | |
    | |
    V2----------R1-----------------------R2-------R2---|GND
     
  2. Figaro

    Figaro Guest

    "N" <caprice24 at no spam yahoo dot com> wrote in message
    | Hi,
    | Note to view the schematic below, change your font to fixed Courier.
    |
    |
    | I have a problem I am trying to work out on simple Op Amps gain,
    | and I am having trouble trying to prove what the gain is.
    | I know what the gain is supposed to be (see below), but
    | I am stumped as to how to actually go about proving it. When
    | I try to setup the Kirchoff node equations I get a really
    | ugly polynomial.
    |
    | I can put the design into a spice deck and prove it, but I want to
    | understand the design from an analytical point of view.
    |
    | Gain = 2*R2/R1 * (1 + R2/Rg)(V2-V1) (GAIN FOR THE OP AMP BELOW)
    |
    | Now looking at the above equation it is obvious if you
    | eliminate resistor Rg, the equation becomes a simple
    | differential amplifier gain, which I can easily solve and
    | prove. However when you add the positive feedback from
    | the output, you get a different Beta for the loop gain
    | that is hard to figure out.
    |
    | Anybody want to take a stab at proving this?
    |
    | Nick ------------
    | | |
    | V1---------R1-----------------------R2-------R2---| |
    | | | |
    | | ___ | |
    | | | \ | |
    | |--Vn| \ | |
    | | \ Vout | Rg
    | | |------------------ |
    | |--Vp| / |
    | | | _ / -----------
    | | |
    | | |
    | V2----------R1-----------------------R2-------R2---|GND
    |

    write the loop equations, apply the following op-amp tricks:

    1) currents into the inputs Vn and Vp are zero because op-amps have very
    input impedance
    2) Vn-Vp is zero because op-amps have very high gain

    and you will get your gain equation
     
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